Two lines are perpendicular if the multiplication of their slopes is equal to -1.
In y =-5/2x + 15 the slope is -5/2, then the slope (m) of the new line is:
-5/2*m = -1
m = -1*2/(-5)
m = 2/5
The slope-intercept form of a line is:
y =mx + b
where m is the slope and b is the y-intercept. Replacing with m = 2/5 and the point (-5,4) into the equation, we get:
4 = 2/5*(-5) + b
4 = -2 + b
4+2 = b
6 = b
Then, the equation is: y = 2/5x + 6
